Modeling Distributions of Data

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Transcript of Modeling Distributions of Data

In this chapter, we learned about describing and identifying normal distributions and how to do standard normal calculations. Cumulative Relative Frequency Graphs Allows you to examine location within a distribution. Helps you estimate & interpret the percentile of a distribution. Normal Distribution Described by a normal curve specified by mean & standard deviationMean is the center of the symmetric normal curve Two ways to measure the position within a distribution Percentiles:Is the value with p percent of the observations less than it.

Z-Score ( Standard Value):•A measure that quantifies the distance a data point is from the mean of a data set. Chapter 2:Modeling Distributions of Data Empirical Rule (68-95-99.7 Rule) Density Curve Has an area of 1 underneath curveAlways on or above the horizontal axisDescribes the overall pattern of a distribution Normal Density Curve(Bell Shaped Density Curve)(Symmetric Density Curve) Skewed Right Density Curve Skewed Left Density Curve Median & Mean of a Density Curve Median: is the equal area point point that divdes the area under the curve in halfMean:Balance pointWhich the curve would balance if made of solid material Mean& Median The long tail pulls the mean to the right. The long tail pulls the mean to the left 68% of the observations fall within of the mean95% of the observation falls within 2 of the mean99.7% of the observation falls within 3 of the mean mean of 0Standard deviation of 1 Standard Normal Distribution 80th percentile 1. Plot the data using a graph: dotplotstemplothistogram 2. Figure out the pattern: ShapeOutliersCenterSpread 3. Calculate a numerical summary to briefly describe center & spread 4. Sometimes a pattern of large number observations can be described as a smooth curve Abbreviate the Normal Distribution with mean & standard deviation asN( , ) 0 + - = 9 8 7 1 2 3 4 5 6 c Standard Normal Distribution Is the normal distribution with a mean of 0 & standard deviation of 1. N(0,1) Using theStandard Normal Table Is a table of areas under the standard deviation The table entry for each value is the area under the curve to the left of z. How to Solve Problems Involving Normal Distributions State: Express the problemPlan: Draw distribution & shade area of interest under curveDo: calculations, Conclude: Write conclusion Transforming Data When adding or subtracting the same number (p) to each observation:(p) would also be added or subtracted to the mean, median, quartiles, percentiles.This would not change the shape or spread. Transforming Data When multiplying or dividing the same number (p) to each observation:(p) would also be multiplied or divided to mean, median, quartiles, percentiles & the spread.This would not change the shape.